Skip to main content

Hypergeometric Functions in Mathematica ®

  • Chapter
  • First Online:
Book cover Computer Algebra in Quantum Field Theory

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

  • 2394 Accesses

Abstract

This paper is a short introduction to the generalized hypergeometric functions, with some theory, examples and notes on the implementation in the computer algebra system Mathematica ®. (Mathematica is a registered trademark of Wolfram Research, Inc.)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Braaksma, B.L.J.: Asymptotic expansions and analytic continuations for a class of Barnes-integrals. Compos. Math. 15, 239–341 (1962–1964). http://www.numdam.org/item?id=CM_1962-1964__15__239_0

  2. Haubold, H.J., Mathai, A.M., Saxena, R.K.: Mittag-Leffler Functions and Their Applications. arXiv:0909.0230 (math.CA)

    Google Scholar 

  3. Marichev, O., Trott, M.: The Wolfram Functions Site. http://functions.wolfram.com (2013)

  4. Meijer, C.S.: Über Whittakersche bzw. Besselsche Funktionen und deren Produkte. Nieuw Arch. Wiskunde 18(4), 10–39 (1936)

    Google Scholar 

  5. Olver F.W.J., et al.: NIST Handbook of Mathematical Functions. Cambridge University Press (2010). http://dlmf.nist.gov

  6. Paris, R.B., Kaminski, D.: Asymptotics and Mellin-Barnes Integrals. Encyclopedia of Mathematics and Its Applications, vol. 85. Cambridge University Press, Cambridge/New York (2001)

    Google Scholar 

  7. Szegö, G.: Orthogonal Polynomials, 4th edn. American Mathematical Society, Providence (1975)

    MATH  Google Scholar 

  8. Zeilberger, D.: A holonomic systems approach to special functions identities. J. Comput. Appl. Math. 32(3), 321–368 (1990)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Oleksandr Pavlyk .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Wien

About this chapter

Cite this chapter

Pavlyk, O. (2013). Hypergeometric Functions in Mathematica ® . In: Schneider, C., Blümlein, J. (eds) Computer Algebra in Quantum Field Theory. Texts & Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1616-6_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-1616-6_10

  • Published:

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1615-9

  • Online ISBN: 978-3-7091-1616-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics